Presents classroom vignettes in which middle grade students with developmentally different views of geometry stimulate each other's reasoning by externalizing mental images through modeling and discourse. (KHR)

The students of a Mathematical Modeling and Problem Solving class investigate and explore the mathematics involved in fitting a box spring mattress up a stairwell by solving various optimization problems and by using The Geometer's Sketchpad. The results show that a very small fraction of the class was actually able to solve the problem without…

The authors recommend introducing complex numbers by first studying the integers modulo seven. (SD)

To measure the effectiveness of a set of instructional materials designed to aid college students in setting up mathematical models of physical situations, undergraduate liberal arts students taking physics were randomly assigned to an experimental group (receiving the materials and using a textbook), a control group (using the text only), or a…

The paper is an en route version of a technical report which will ultimately present a process model of transfer that will be usable in the design of instructional programs. Consequently, it is a progress report with respect to the formulation of that model. (LI 004 279 and 004 280 are related documents) (Author)

Describes a combination of lectures, experiments, and analysis with the aid of remote computer terminals that helps the engineering student grasp the fundamentals and implications of a mathematical model applied to a particular job situation. (MLH)

An analysis of methods of teaching children to solve verbal arithmetic problems is presented together with transcriptions of interviews in which children solve problems by reference to problem types. (SD)

Demonstrates that if a sinusoidal oscillation of the point of support of a pendulum is approximated by a square wave, a matrix method may be used to discuss parametric resonance and the stability of the inverted pendulum. (Author/SL)

A model for division of fractions using money as manipulative material is presented. Eight levels are described, ranging from the development of language and concept introduction through types of problems to rule discovery and application. (MNS)

A three-dimensional model made from pegboard, rods, and spheres can be used to illustrate principles of multi-variate analysis. (SD)

In this paper are described some features of the intensive use of math software, primarily Derive, in the context of modeling in an introductory university course in differential equations. Different aspects are detailed: changes in the curriculum that includes not only course contents, but also the sequence of introduction to various topics and…

The National Science Education Standards (NSES) emphasize the use of models in science instruction by making it one of the five unifying concepts of science, applicable to all grade levels. The NSES recommend that models be a focus of instruction--helping students understand the use of evidence in science, make and test predictions, use logic, and…

Some single species and two species interactions in population models are presented to show how credible examples can be used to teach an underlying, common mathematical structure within apparently different concepts. The models examined consist of differential equations, and focus on real-world issues. (MP)